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The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power .
This approximate formula is for moderate to large sample sizes; the reference gives the exact formulas for any sample size, and can be applied to heavily autocorrelated time series like Wall Street stock quotes.
For a confidence level, there is a corresponding confidence interval about the mean , that is, the interval [, +] within which values of should fall with probability . ...
Factors affecting the width of the CI include the sample size, the variability in the sample, and the confidence level. [2] All else being the same, a larger sample produces a narrower confidence interval, greater variability in the sample produces a wider confidence interval, and a higher confidence level produces a wider confidence interval. [3]
According to this formula, the power increases with the values of the effect size and the sample size n, and reduces with increasing variability . In the trivial case of zero effect size, power is at a minimum ( infimum ) and equal to the significance level of the test α , {\displaystyle \alpha \,,} in this example 0.05.
= the number of data points in , the number of observations, or equivalently, the sample size; k {\\displaystyle k} = the number of parameters estimated by the model. For example, in multiple linear regression , the estimated parameters are the intercept, the q {\\displaystyle q} slope parameters, and the constant variance of the errors; thus ...
Given an r-sample statistic, one can create an n-sample statistic by something similar to bootstrapping (taking the average of the statistic over all subsamples of size r). This procedure is known to have certain good properties and the result is a U-statistic. The sample mean and sample variance are of this form, for r = 1 and r = 2.
Since the sample does not include all members of the population, statistics of the sample (often known as estimators), such as means and quartiles, generally differ from the statistics of the entire population (known as parameters).